A galvanometer of resistance G is converted into a voltmeter of range $0-$ IV by connecting a resistance $\mathrm{R}_{1}$ in series with it. The additional resistance that should be connected in series with $\mathrm{R}_{1}$ to increase the range of the voltmeter to $0-2 \mathrm{~V}$ will be:

(A) $\mathrm{R}_{1}+\mathrm{G}$

(D) $\mathrm{R}_{1}-\mathrm{G}$

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Current Electricity

A galvanometer of resistance G is converted into a voltmeter of range

0 -

IV by connecting a resistance

R_{1}

in series with it. The additional resistance that should be connected in series with

R_{1}

to increase the range of the voltmeter to

0 - 2 V

will be:

Answer: (A)

A galvanometer of resistance

G

reaches full scale at a current

I_{G}

. For the

0

1

V range,

1 = I_{G} (G + R_{1})

. Adding a further series resistance

R_{2}

to reach the

0

2

V range gives

2 = I_{G} (G + R_{1} + R_{2})

. Subtracting the first relation from the second leaves

1 = I_{G} R_{2}

; but

I_{G} (G + R_{1}) = 1

as well, so the two right-hand sides are equal and

R_{2} = G + R_{1}

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Single correct option